Evolution of trust in the N-player trust game with transformation incentive mechanism

Trust game is commonly used to study the evolution of trust among
unrelated individuals. It offers valuable insights into human interactions
in a variety of disciplines, including economics, sociology, and
psychology. Previous research has revealed that reward and punishment
systems can effectively promote the evolution of trust. However, these
investigations overlook the gaming environment, leaving unresolved the
optimal conditions for employing distinct incentives to facilitate trust
level effectively. To bridge this gap, we introduce a transformation
incentive mechanism in an N-player trust game, where trustees are given
different forms of incentives depending on the number of trustees in the
group. Using the Markov decision process approach, our research shows that
as incentives increase, the level of trust rises continuously, eventually
reaching a high level of coexistence between investors and trustworthy
trustees. Specifically, in the case of smaller incentives, rewarding
trustworthy trustees is more effective. Conversely, with larger
incentives, punishing untrustworthy trustees is of greater efficacy.
Furthermore, we find that moderate incentives positively influence the
average payoff within the group.